## Calculating modulus of elasticity?

I'm trying to figure out how to calculate the modulus of elasticity for a board clamped to a surface plate at one end and free-floating on the other. I've measured the deflection with a 1k weight at the free end of the board. So I've got that data as well as the dimensions of the free-hanging portion of the board.

I've done this test with numerous boards of different thicknesses and dimensions and want to compare them in terms of stiffness.

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 Recognitions: Gold Member Homework Help Science Advisor Hi tobyrzepka, welcome to PF. Try a search for "beam bending equations" to find the deflection vs. Young's modulus for a number of different boundary conditions. For the case of a cantilevered beam (clamped at one end, transverse load on the other), the deflection is $\delta=PL^3/3EI$, where $I=wt^3/12$ is the second moment of area. Does this answer your question?
 Like Mapes stated correctly, δ=F*L^3 / 3E*I Since you measured deflection you can solve as E (elasticity modulus) and you'll have it. E=I*F*L^3 / 3δ F = Force applied (1kg as you mentioned) L = Length (Length of each board) E = Elasticity modulus (You will do the math) I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness) δ= Deflection (As you measured) I hope that helped

## Calculating modulus of elasticity?

So you said :
I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness)

I assume you meant b = width of the board, and h = height... is that right?

 Quote by polymerou Like Mapes stated correctly, δ=F*L^3 / 3E*I Since you measured deflection you can solve as E (elasticity modulus) and you'll have it. E=I*F*L^3 / 3δ F = Force applied (1kg as you mentioned) L = Length (Length of each board) E = Elasticity modulus (You will do the math) I = Inertia moment (b*h^3)/12 where h=width of board and h=height (thickness) δ= Deflection (As you measured) I hope that helped

 b=width, h=depth/height for a rectangular section I =(b.h^3)/12